We analyse long-term consumption paths in a dynamic two-sector economy with overlapping generations. Each young generation saves for the retirement age, both with private savings and pension funds. The productivity of each sector can be raised by sector-specific research while the essential use of a non-renewable natural resource poses a threat to consumption possibilities in the long run. Bonds, the two types innovations, and resource stocks are the different investment opportunities. We show that pension funds have a positive impact on long-term development, provided that individuals have a preference for own investments. In this case, sustainability is more likely to be achieved due to pension fund savings.